Wilshere, 21, returned from more than a year out injured in October but is already being heralded as an integral part of England's future following his man-of-the-match display in the 2-1 win over Brazil at Wembley on Wednesday night.
Wenger knows the progress of the combative midfielder must be carefully handled if both Arsenal and England are to see the best of the player over the long term.
"It is not just the physical aspect, but the mental pressure every time he plays. We will have to manage him well physically to make sure he doesn't face that burnout," said Wenger, whose side resume Barclays Premier League action at Sunderland on Saturday.
"I had in fact expected Jack to play only a part of the game on Wednesday, but it didn't happen and because of his quality he will be exposed to that, the overuse of his quality, and you can understand that.
"He will have to be managed like everyone else.
"Let's not forget that he is only 21 now, and he starts his career really because he was out for 17 months.
"The influence he has today on the England national team already is absolutely fantastic."
England captain Steven Gerrard is in no doubt Wilshere can become one of the greatest players of his generation, while manager Roy Hodgson claimed "you can crank up the expectations as much as you like" following his Wembley heroics in midweek.
Wenger is happy to allow Wilshere, who joined Arsenal at the age of nine, to see his game develop naturally - albeit amid the glare of heightened public expectation.
"You do not want to set any limit on the development of any player, especially when he plays at that level at his age," Wenger said.
"The most important thing for me will be to keep his passion for the game, and keep the attitude of wanting to become a better player.
"If he keeps these two ingredients that are not always easy, he can of course become a fantastic player. He is already one, but he can become one of the best in the world, yes."
Academy head Liam Brady helped bring Wilshere through the Arsenal ranks but is set to step down from his role in May 2014.
Wenger revealed the recruitment process for a successor to the Gunners legend is already under way, with ex-captain Patrick Vieira, now the football development executive at Manchester City, and Dennis Bergkamp both linked with the role.
Wenger said: "Patrick Vieira can be a candidate if he wants to do it. All the former players are of course candidates.
"What is the most important for me is the competence of the person and the experience in this kind of department. It is a very specific and special job,"
Wenger says he is likely to have to be "creative" in defence at Sunderland tomorrow, with captain Thomas Vermaelen still sidelined by an ankle problem and Laurent Koscielny facing a fitness test on the calf injury he picked up while away with France.
Ignasi Miquel, the 20-year-old Spaniard, is on standby.
There are no such issues in attack, with Theo Walcott, Olivier Giroud and Lukas Podolski forging a formidable frontline.
"I was not convinced at the start of the season that I would play them all together," Wenger said. "I am happy that, slowly, they understand each other well and we are efficient in goalscoring - we have scored more goals than last year."
Arsenal are currently sixth, a point behind Everton and four adrift of Tottenham - two sides they have still to play again.
Wenger still has confidence his men can force their way back into the Champions League places.
He said: "We do not have to look at the others, just win our games because we are behind and therefore we just focus on trying to win."
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